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2.Diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area?


Answer :

Cylinder B will have a greater volume.
Verification:

Volume of cylinder A=\(\pi r^2h\)

\(=\frac{22}7\times \frac{7}2\times\frac{7}2\times 14\)

\(=539cm^3\)

Volume of cylinder B=\(\pi r^2h\)

\(=\frac{22}7\times7\times7\times 7\)

\(=22\times49=1078cm^3\)

So, we can see that cylinder B has more volume.Hence the assumption was correct.

Now comparing the surface areas of both the cylinders:

Total surface area of cylinder A=\(2\pi r(r+h)\)

\(=2\times\frac{22}7\times\frac{7}2(\frac{7}2+14)\)

\(=2\times\frac{22}7\times\frac{7}2\times \frac{35}2\)

\(=385cm^2\)

Total surface area of cylinder B=\(2\pi r(r+h)\)

\(=2\times\frac{22}7\times7(7+7)\)

\(=2\times\frac{22}7\times7\times 14\)

\(=616cm^2\)

Hence we can observe that cylinder B has more surface area.